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Within the HSR universe, the luck of the draw is a force that exerts considerable influence on the game's story, whether it comes from main story quests, to places as easily overlooked as readables or an obscure description in a location rarely ventured anymore. As I touched on in a previous meta of mine, there are considerable confluences and means of interference that can alter a seemingly fixed segment of the story. Through the Solitary Waves Theory, expounded on in Antimonic Waltz, we're essentially told that any and every Path has the potential to "rewrite the constant" and change the future of the universe.
However, I do believe there's a stark difference between doing this by chance and having the ability to alter the future intentionally. Probability manipulation is a very deliberate ability I think merits exploring, especially through the people who are the most prolific examples of it.
As the LC Destiny's Threads Forewoven states, the ability to manipulate fate is the domain of destiny itself, which makes these two's abilities even more interesting.
Asat Pramad
The trace materials Four Phases, Crossing the River to Check the King & Omnicolor, Fool's Own, as well as the retconned DU curio, Asat Pramad's Dice (Head), all paint an identical picture: that the Lord Ravager is capable of controlling probability in order to manipulate the outcome.
In So Laughed the Masses, Serotonin Exposure Phobia, this control is crystalized when Asat tells us to our faces that he has the ability to control probability through the power of Elation, one that has already proven its ability to change causality and tilt an instance towards chaos.
Elation Brimming With Blessings, an Elation Light Cone, seems to prove this notion. An element of Asat's probability manipulation is that it isn't without an element of chaos. As it's derived from Elation, this unpredictability is tempered by his dice that do allow him some control. But, this kind of control doesn't mean expected results, so much as changing an outcome until it grants him one he wants; as stated in the relics, this lack of full control may be intentional, instead rerolling until a more favorable outcome is achieved.
Whether this means Asat's probability manipulation isn't total or slightly unpredictable on purpose might not be fully known, but if the Navigator's Everstride Boots are anything to go by, he may not have as much control as we think, but learned to use it to his advantage.
Polka Kakamond
As a towering figure within the game's lore, Polka's existence was as known as far back as the prologue mission when Kafka had the option of examining her portrait in Herta's office on the way to "dropping off" Trailblazer at the start, positioning them where they needed to be.
Although it wasn't known until a little later on, Polka's ability to manipulate probability and causality are legendary.
The process is best described in the SU/DU curio, Kill That Butterfly, believed to be narrated by Polka herself as she muses on how she controls causality. In doing so, she's described as "annihilating a chaotic system" whereby she compares this manipulation to insect taxidermy that involves pinning a specimen; in this case, it's a butterfly likely as a metaphor for the butterfly effect.
In Pom-Pom's Intel | Unveiling the Dangerous Members of the Genius Society, and in Overviewing the Ripples of the Unknowable Domain, it's also made clear that Polka's causality manipulation is informed by Nous' "moments" that help her formulate a strategy behind her assassinations and other modes of interference.
While Asat Pramad's means of probability control are driven by an element of chaos, Polka's eliminates all of it (or, it tries to). As Herta speculates in Antinomic Waltz, this causality control may extend far and wide, leading her to believe that Polka herself may be the one running interference. With her causality manipulation so staggering, it makes one wonder as to the full extent of her abilities, and how far-reaching they truly are.
Conclusion
While not a common ability, and with the likelihood of other people within HSR bearing such an ability, it nonetheless makes for an extremely interesting study with how much emphasis is given to destiny and the ability to either control or defy it.